Eibar equalised five minutes after the break when Ivan Ramis headed home from Pedro Leon’s corner.
Ronaldo’s bullet header from Dani Carvajal’s cross in the 84th minute earned Madrid the three points.
Zidane told his postmatch news conference that Eibar had been on top for much of the game, hailing his players’ battling qualities.
“The opponent was very superior today, above all in the first 25 minutes when we barely left our own half,” he said.
“We knew this was a tough place to come – they are having a good season. Today we had difficulties with the ball, technically we made a lot of mistakes in our passing, playing out from the back.
“There are days when we do not do play so well. But we showed other things today, character, we all fought together.”
Ronaldo has scored in his last seven appearances in all competitions, and Zidane said: “He is from another galaxy.
“What he has is so positive – he knows he is going to score. He is a different player, special. His stats speak for themselves.
“We did not play at our best, but Cristiano knows what to do — with few chances he can score many goals.”